It’s not often that you find truly notable people in history. It requires more than mere accomplishment. Moral convictions, passion, and awesome stories must all accompany a person’s legend in order for their tale to be considered epic. Here are five simple reasons that Alexander Grothendieck’s story is one of the most epic around.

5) He decided to study math because someone told him there were no more major problems left to solve. As his way of responding to this statement, he revolutionized the entire field multiple times. Due to this, he is often called “the master thinker.”

4) He got interested in math during high school, while in France, running away from Nazis. This is not an exaggeration.

3) Grothendieck received a prestigious reward in 1988 that was accompanied by a huge cash prize. Alexander’s response, of course, was to decline it. He stated that there were two major reasons for this. First, he didn’t need the money, and thought the rich taking more money was immoral. Second, the entire scientific community was ethically up their own butts. Enough said.

2) He was one of the world’s most stunning mathematicians. Beyond taking abstract math to all new levels of thought, he created foundational principles on scheme theory, nilpotent numbers, topological theories, and created a proof on something for which a proof should have been impossible. Of course, he was used to doing impossible things by then.

1) Many people with strong political beliefs aren’t willing to take action on their convictions, especially when it might put them in the line of fire. Not so for Grothendieck! It’s true, what he really knew how to do was math, so he gave some anti-War lectures in Vietnam during the Vietnam War. What is unique about these lectures is that they happened just outside the city of Hannoi. Oh, did we mention that Hannoi was being bombed by the United States at the time?

Yes, it’s official. Alexander Grothendieck is one of the coolest people throughout history, and certainly more of a guns blazing sort than most mathematicians.

In the 20th century there have been some truly influential mathematicians, and Alexander Grothendieck is one of them. He has made some important revolutionary advances in a number of different areas of mathematics, including homological algebra, category theory, functional analysis, number theory and algebraic geometry. Grothendieck is particularly known for his rather abstract approach to the concept of mathematics. He was a perfectionist, but also capable of using general mathematical methods to derive the most concrete results.

There are constant advances in mathematics, and these advances can lend themselves to a variety of different uses and purposes, including determining auto insurance rate quotes for consumers today. Mathematics are used every day throughout society, and while most everyday mathematics are not as advanced as what Alexander Grothendieck was known for, he has certainly had an impact on today’s mathematics.

Mathematics may be as simple as addition, subtraction, multiplication and division, or mucfh more complex. We use mathematics when we make purchases or run businesses, when we file taxes, when we make investments and when we insure our assets. Our assets involve mathematics when we determine their costs and value. Everything we own has been impacted by mathematics in some form or another, and everything we will own in the future will also be impacted by both basic and complex forms of mathematics.

You cannot likely live a single day without using math in some form or another. When you cook, you use math to read and interpret recipes. When you drive, you use math when appraising your speed or checking your gas gauge. When you make purchases, you use mathematics to determine sale prices, sales tax and discounts. At dinner you use mathematics to determine how much to tip your waitress. Mathematics is all around us, and our understanding of these mathematical concepts comes from the advances of the past, such as those from Alexander Grothendieck.

Math is full of challenges and rewards by its very nature, but these are magnified when you put it at the center of a competition. While it may not receive the glamorous media attention of modern sports, competitive mathematics is an increasingly popular form of recreation. Here are a few of the active and ongoing competitions you can engage in.

The Canadian Mathematical Society features a number of different competitions. Of note are the Canadian Open Mathematical Challenge, which takes place annually in November, and is open to all high school students; the Canadian Mathematical Olympiad, where qualifiers from the Open and winners from other mathematics competitions are invited to face off for a large cash prize; and the International Mathematics Olympiad.

Unsolved Problems is a site that presents deeply complex mathematical issues that have yet to be resolved. Much of the informational available is presented directly on the website, and some of the problems feature a reward for the first to complete a proof or find a solution. A total prize pool of seven million dollars is available for any who solve these major problems.

The New Brunswick Math Competition is highly beneficial for both students and schools due to its structure. In addition to awarding prizes for top competitors, the framework utilized allows Universities to get in touch with students reaching the end of the secondary school education.

International Mathematics Talent Search is a group devoted to finding the best and the brightest within the field. This forty-four round problem solving competition helps find to locate these great minds, and often directs them to more exclusive competitions, higher education, and greater opportunities.

America has its own math contest, the MAA (American Mathematics Competition), which provides an in-depth online forum and a large number of useful resources for competitors and potential competitors. This competition includes regional and national stages, allowing competitive math gurus to start their journey to triumph more locally.

There are also many local competitions. These are generally sponsored by Universities, and have either cash prizes or award scholarships. There are online lists of regional math competitions in North America.

Alexander Grothendieck is well known in the advanced mathematical community, especially for his work within theoretical vectors and algebraic geometry. He was significant enough that several mathematical properties or groupings have since been named after him. This entry lists the fundamental advances and foundational work laid out by Grothendieck during his mathematical and academic career.

The original thinker behind homological and sheaf theory within geometry was Jean-Pierre Serre, who worked off of the ideas of Jean Leray and Kiyoshi Oka. Grothendieck took it a step further, however, by adding expanding on the tool set and altering the degree of abstraction used. He made a fundamental paradigm shift within conceptual mathematics by moving the study from individual types to groups of types for the purpose of generalization within many theories. He applied it to other major theories in published works starting in the 1950s.

He began other foundational work by working at higher levels of abstraction than had ever been seen previously in functional theories. He used what were known as “non-closed generic points” in his work, which led to the concept of schemes.

Grothendieck was one of several mathematicians at the time who created the foundational work of systematic nilpotents which carry either the value of zero or infinitesimal data, dependent on their role in an algebraic equations. It was the concept of schemes which worked as the foundation for this principle, and even today it is widely accepted as the best approach due to its immense depth and utility. The schemes theory is also powerful for its ability to integrate commutative algebra, topology, number theory, and birational geometry. This work was fundamental for later concepts, including the development of D-modules in later mathematics.

Grothendieck also invented theories that explain the connection between topological and number theoretic characteristics. His exploration of the relationship between finite equations and their topological nature was executed via a new set cohomological theories, and explained previous complex observations that did not have viable proofs.

Mathematics is considered an unwanted burden by many high school students, and a large portion of them complete their minimum requirements and then abandon the field entirely. The exceptions are far too often those who want to get rid of their minimum college requirements as well. This “minimum requirement” approach is ineffective for those who seek to reap the many rewards of math in the remainder of their life, and truly, there are many.

Reason #1: You’ll get into college more easily.

If you are intending to move on to University study, then having a focus in math during high school, or better yet a math major, will help in admissions to almost any college. A devotion to mathematics is seen as highly appealing by most academic groups.

Reason #2: It prepares you for valuable, highly paid, and rewarding work.

Much of the work that math will prepare you for, including the scientific and mechanical engineering fields, are have numerous in-demand jobs that have you solving vital problems and receiving a hefty paycheck for it. In a job market as competitive as that of today, having such a marketable skill is deeply worthwhile.

Reasons #3: Math fine tunes your brain.

Learning higher degrees of math will help your brain function at a higher level, more rapidly solving problems and seeing creative solutions. No matter what job path you choose to take, having a background in math will help improve your overall performance.

Reasons #4: It prepares you to defend your wealth in the real world.

Beyond paying you more, mathematics will help you understand good and bad investment strategies. Beyond just helping you choose the right stock program and balance numbers appropriately, it can help you sidestep foolish ways of spending your money, such as multilevel marketing jobs.

Reasons #5: Mathematics are an unchanging foundation to a changing world.

The world is quickly moving on to new concepts and technologies with each passing year. If you understand mathematics, you will understand how and why these changes occur, and will be more prepared to live in the fast paced modern era.

Believe it or not, great minds have been challenging themselves with advanced math problems at least four thousand years now. The earliest recorded mathematical challenge is from a papyrus scroll dated back to about 1850 BC. These math puzzles continue to stimulate the minds of young mathematicians. Here are a few of these excellent puzzles.

We will begin with the one located on the papyrus. Here is a paraphrase of what that Egyptian mind teaser said: There are seven homes, and in each there are seven cats. Each one of these cats eats seven mice. These mice had each eaten seven ears of grain. Each one of these ears of grain would have produced a total of seven hekats of wheat. How much wheat would have been produced had the grain been left to grow?

Fibonacci, while famed for his sequence, was also a fan of bunnies, at least for the sake of a mathematical puzzle. He created this problem: Let us say a man put two bunnies in a room. Then, let us assume that each pair produces a further pair of bunnies, and that each of these pairs becomes productive toward procreation on its second month, while the original pairs remain productive. How many bunnies would there be at the end of a year?

Math boards have also been used for puzzles such as these. One Guarini di Forli took a three square by three square board and placed two white and two black knights in the corners of it. He then posed a simple puzzle: using the rules that are normal for knights in the game, how can these colors of knights switch sides?

Bachet is famous for his “weighing problems,” including the “weighing pan problem.” The problem can be paraphrased as this. First, assume that there is a weighing pan with two sides, and that weights can be put on one side to subtract from the other. What is the very smallest number of weights that can be used in order to have a scale and weight system which can weigh any whole number between one and forty?

If you’ve already been won over to the simple beauty of a correctly applied and aptly resolved mathematical problem, you don’t need any further explanation for how math can be used recreationally. You may already know just how enjoyable it is to seek out and solve problems in a structured format that isn’t being shoved down your throat by a teacher. If you are a part of that crowd, or are interested in joining it, here are a few ways to spend some time having fun with math.

Cut the Knot is one site that offers a number of different games and learning tools for users who are interested in devouring more knowledge. While the site features some fun tools for people who are getting involved in simple geometry and arithmetic, the truly fascinating portion of the site resides elsewhere. A few sections of note include the following.

“Eye Openers” are visual exercises that challenge you to accomplish tasks as efficiently as possible. Here, games like the chocolate bar breaker force you to break apart a rectangular bar of sweets into the correct number of segments with as few total breaks as possible. Pattern finding equations that translate numbers into words and letters, geometrical games that force you to mimic lines, and other visual games all prompt users to learn through entertaining application.

The “Social Sciences” section takes practical application to a new level. By walking you through stories which take real life problems, including some significant historic story based issues, these games show the real value of math in the real world. Practical application rarely has such a sense of reward as when you save the (imaginary) world with them.

The Fallacies section is great for those who love neck deep conundrums. It features a number of paradoxes, and prompts users to use math to find appropriate solutions, or explore alternative solutions or presentation methods which fix the fallacy appropriately.

There are other sites with great games, too, but Cut the Knot is one of the most stable and long lasting out there. We encourage you to explore these and other options.

Famous mathematician Alexander Grothendieck may have published many more scientific works if it wasn’t for his withdrawal from the scientific community in 1970. This withdrawal was not one of exhaustion or completion, however, but one of activism. Grothendieck’s actions were calculated, and were all part of a much larger picture of radical political activism that took a high priority throughout his life.

Grothendieck’s parents provided the foundation of his political outlook. Both his Jewish father and German mother were anarchists, and left the country when Alexander was just a child, in part to fight in the Spanish civil war. During his teenage years, Grothendieck lived in sheltered camps to escape from the Nazi faction. His father was not as successful, and died in Auschwitz.

These significant events throughout his childhood formed the foundation for his radical views. He thought of himself as a radical anarchist, with strong pacifistic sentiments. This meant that he stood in strong opposition to both capitalist America’s actions in Vietnam and Soviet expansion. He did not stop at simply believing his convictions to be correct, however. Among other political protests, Grothendieck taught lectures in the forests surrounding the Vietnamese city of Hanoi while it was actively being bombed.

It was this political activism that led him to leave the IHES, the group funding most of his research. He left stating the cause for his departure was discovering the military funding, and some military applications, or research at IHES. While this is likely true, it is also not the full story. Due both to his background and his views as a class struggle anarchist, Grothendeick always related very deeply to the poor and downtrodden, and his presence in the scientific community felt caging.

After his departure from IHES, Grothendieck worked as a professor at the University of Montpellier until 1988. He continued writing on politically heated topics, and launched direct criticisms of the scientific community for what he viewed as its ethical compromises. These same ethical compromises prompted him to publicly decline the Crafoord Prize in 1988. His writings became minimal after 1991, but still contained political overtones.

Mathematics is a field of human exploration and discovery, where abstract thought meets practical reality head on. This has resulted in countless equations, numerous in-depth forms of study (such as algebra, geometry, calculus, statistics, topology, homology, and so forth), and the creation or discovery of numbers with very specific mathematical numbers. Here are the most fascinating numbers in math.

Pi is the best known of the fascinating numbers. Many even have the first portion of this sequence (3.14159) committed to memory. Pi has more practical application than almost any other single irrational number, and is used for calculations involving abnormally shaped or round objects. This makes it fundamental in modern engineering.

The number known as “e” is named after the Leonhard Euler, who originally discovered it. This number has vast implications in modern business and investment, as well as growth mathematics. The irrational number e begins with 2.718, and represents the maximum end result for an item that grows off of its own gains.

Let’s take a simple example of what this means and how it applies. Let’s say that you invested a thousand dollars in a banking institution, and their growth rate allowed that thousand dollars to become two thousand dollars over the course of twelve months. Leaving it there for twelve months is insufficient, however, for maximum results. Simply withdrawing it after six months and immediately redepositing the new amount, for example, would increase your end total by $250. E is the top result possible here. In this case, it would mean $2718 after a year, with appropriate deposits and withdrawals.

The final number we will discuss today is the number i, or the symbol for the square root of negative one. This number began seeing use in the 1800s as different physical phenomena were being analyzed for their complex mathematical properties. The math behind electricity and electric circuits, dampening fields, flowing fluid, object resilience, and more are best understood through imaginary numbers. Even in study where i is not strictly necessary, it can be used to dramatically simplify bulky or complicated problems.

If you’re deep into mathematics, you may have run into the name “Grothendieck,” if only because of Grothendieck topology. As with everything, however, the title has a story, and this one roots back to a man named Alexander Grothendieck – a German born mathematician who revolutionized modern concepts of algebra based geometry.

Grothendieck was the child of Alexander Shapiro and Johanna Grothendieck, both anarchists who broke from their religious backgrounds during their early adulthood. While Alexander was originally born with the first name “Raddatz” due to his mother’s first marriage, it was soon revealed that Shapiro was the father, so Alexander adopted his mother’s last name. He lived with them only until the age of five, at which time he shifted to the care of Wilhelm Heydorn, who saw to his education.

While Alexander’s Jewish father died at Auschwitz during World War II, Alexander himself lived safely with his mother in France, residing in camps for displaced persons for a time, following which he took up secret residence in Le Chambon-sur-Lignon village. While there, he attended the secondary school Cévenol, where he first became interested in mathematics.

By the end of his secondary education, Alexander was certain that mathematics was the appropriate course for his life, so he traveled to Montpellier to attend University and continue his studies. He decided to teach mathematics because he was told that all the math problems had already been solved earlier in the century. His creative mind, definite talent, and friends prompted him to change his course and go to Paris to see if there were any new answerless questions in the field.

He spent time in Paris and subsequently at the University of Nancy studying vector topology mathematics. Within a few years, he became the leading expert on the subject. From there, he moved on to more in-depth research on a variety of other topics, beginning a career lined with discoveries and mathematic paradigm shifts.

Grothendeick left the mathematic community, partially for political reasons, but continued to write until 1991, when he retired and withdrew from the public eye. As of this writing (August, 2010) he is still alive.